In general, a measurement result typically includes some portion or contribution attributable to the desired signal of interest, and some portion attributable to noise, jitter, and/or interference. Based on the magnitude of the signal of interest relative to the magnitude of noise, jitter, and/or interference, the sensitivity and accuracy of the measurement are limited. The measurand generally cannot be measured accurately if the signal-to-noise ratio (SNR) or signal-to-noise-plus-interference ratio (SNIR) is less than one. However, special techniques can be used to limit the effective bandwidth of the measurement process to regions where the signal is high and noise is low, thereby effectively increasing the signal-to-noise ratio and increasing the ability to extract the true value of the measurand from the noisy measurement result. For example, simple averaging can be used to increase the effective signal-to-noise ratio in some cases, especially in the case of white noise. Unfortunately, in many cases, the dominant noise is not white noise and simple averaging may not be effective. Therefore, more sophisticated techniques are generally needed to recover the signal.
A lock-in amplifier is commonly used to measure or extract the amplitude and phase of the measurand in a modulated signal that is accompanied by a significant amount of noise and/or interference. In general, lock-in amplifiers require modulated signals, and such modulation may be achieved by using a chopped incident beam. A lock-in amplifier makes use of a priori information describing the modulation of the signal, in the form of an internal reference signal or waveform corresponding to the modulation waveform of the signal, to recover or extract the signal from the noise. A lock-in amplifier mixes (multiplies point-by-point) the measured input signal with the internal reference signal waveform, and integrates the result of this process over a specified time interval, which can be chosen according to the signal and noise characteristics present in the system, the desired accuracy and precision of the measurement, and the time allowed for the measurement. The result of the integration may be seen as an essentially-DC signal which corresponds to the amplitude of the original signal before modulation. Contributions from any source of noise, interference, or perturbation that are not at the same frequency and/or phase as the internal reference signal are effectively cancelled, as the integrated result of the mixing process from these contributions will approach or tend toward a zero value. Offset or baseline errors in the signal measurement channel will also be eliminated, because the reference waveform has an average value of zero. Importantly, chopping and lock-in amplification allow for the reduction of 1/f noise which dominates many experimental systems at lower frequencies. By modulating the signal, the experimental system can be effectively removed from the region where 1/f noise sources dominate.